Difference between revisions of "Tangent approximation"
Jump to navigation
Jump to search
| Line 7: | Line 7: | ||
<math> y - y' = \frac{dy}{dx}\ x - x'</math> | <math> y - y' = \frac{dy}{dx}\ x - x'</math> | ||
| − | When one point on the curve is known, | + | When one point on the curve is known, x and y values are plugged into <math> \frac{dy}{dx}\ </math> to find the slope at a particular point, and the coordinates of the point are plugged in for <math> (x',y') </math> |
Revision as of 13:31, April 5, 2008
The tangent approximation method is a method in Calculus employed to find the equation of a line tangent to the curve. One must know the slope of the curve and a point on the curve. The slope is usually found by taking the derivative of the equation and equating it to the change in y over the change in x:
<math> \frac{dy}{dx}\ = \frac{rise}{run}\ = \frac{y - y'}{x - x'}\ </math>
Utilizing cross-multiplication, this yields:
<math> y - y' = \frac{dy}{dx}\ x - x'</math>
When one point on the curve is known, x and y values are plugged into <math> \frac{dy}{dx}\ </math> to find the slope at a particular point, and the coordinates of the point are plugged in for <math> (x',y') </math>